Let p be an arbitrary polynomial
p(x) = anxn + an-1xn-1 + ... + a1x + a0, an cannot equal 0.
a) Find (dn/dxn)[p(x)]
b)What is (dk/dxk)[p(x)] for k>n
The Attempt at a Solution
Im actually not really sure what to do for this question.
For the first part i tried to take the first three derivatives and got
(d/dx)[p(x)] = a1
(d2/dx2)[p(x)] = 2a2x + a1
(d3/dx3)[p(x)] = 3a3x2 + 2a2x + a1
(dn/dxn)[p(x)] = nanxn-1 + (n-1)a(n-1)xn-2 + ... + a1
Thats my guess, I am not sure of how to do it.
As for part b:
I don't even know how to approach this question, my only assumption is that its the same answer again with all the n's replaced with k's. I am certain this is wrong so please help me do this question both a and b. Thank you.